Large deviations for Langevin spin glass dynamics
type: Item
instance of: scholarly article
title: Large deviations for Langevin spin glass dynamics
zbMATH Open document ID: 0830.60017
DOI: 10.1007/BF01198846
author: Gerard Ben Arous
author: Alice Guionnet
publication date: 1995-12-05T00:00:00Z
review text: The authors study the thermodynamic limit (i.e., the number of spins tends to infinity) of an asymmetrical spin glass dynamics defined by a random mean field interaction. This type of Langevin dynamics was introduced by \textit{Sompolinsky} and \textit{Zippelius} [Phys. Rev. 25, 6860 (1983)] for a continuous version of the Sherrington-Kirkpatrick spin glass model. In contrast to the physics paper, the dependency in the coupling matrix, given by the symmetry, is dropped as a simplification. Results: For high temperatures a full large deviation principle for the annealed law (i.e., averaged over the disorder in the coupling matrix) of the empirical measure on the path space is proved. The corresponding rate function attains its minimum at a unique probability measure \(Q\) on the path space, which is the law of a non-Markovian process. From this the convergence of the quenched law (i.e., for almost all realisations of the coupling matrix) of the empirical measure to \(\delta_Q\) is deduced. The study of the quenched behavior of a single spin is started by the investigation of a dynamics for a replicated system of interacting spins.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 82C44
zbMATH DE Number: 800491
zbMATH Keywords: thermodynamic limit
zbMATH Keywords: asymmetrical spin glass dynamics
zbMATH Keywords: Langevin dynamics
zbMATH Keywords: large deviation principle
zbMATH Keywords: empirical measure
zbMATH Keywords: interacting spins
MaRDI profile type: Publication
cites work: Some rigorous results on the Sherrington-Kirkpatrick spin glass model.
cites work: Methode de laplace: etude variationnelle des fluctuations de diffusions de type
cites work: Large deviations from the mckean-vlasov limit for weakly interacting diffusions
cites work: Q4692653
cites work: Prescribing a System of Random Variables by Conditional Distributions
cites work: Calcul stochastique et problèmes de martingales
cites work: Q3997990
cites work: Q4237477
cites work: Q3999495
cites work: Q3997782
cites work: Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated
cites work: �quations de type de Boltzmann, spatialement homog�nes
full work available at URL: https://doi.org/10.1007/bf01198846
OpenAlex ID: W4248270741
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 800491